The correction methods include the Bonferroni correction (bonf)
in which the p-values are multiplied by the number of comparisons.
Less conservative methods are also included such as Sidak (1967)
(sidak), Holm (1979) (holm), Benjamini & Hochberg (1995)
(fdr_bh), and Benjamini & Yekutieli (2001) (fdr_by), respectively.

The first three methods are designed to give strong control of the
family-wise error rate. Note that the Holm’s method is usually preferred.
The fdr_bh and fdr_by methods control the false discovery rate,
i.e. the expected proportion of false discoveries amongst the rejected
hypotheses. The false discovery rate is a less stringent condition than
the family-wise error rate, so these methods are more powerful than the
others.

The Bonferroni adjusted p-values are defined as:

\[\widetilde {p}_{{(i)}}= n \cdot p_{{(i)}}\]

where \(n\) is the number of finite p-values (i.e. excluding NaN).

The Sidak adjusted p-values are defined as:

\[\widetilde {p}_{{(i)}}= 1 - (1 - p_{{(i)}})^{n}\]

The Holm adjusted p-values are the running maximum of the sorted
p-values divided by the corresponding increasing alpha level: